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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Quadratic Forms 4-9
2. x
2
+ y
2
+ z
2
2xy + 2xz 2yz
Ans:
111
11 1
111
⎡⎤
⎢⎥
−−
⎢⎥
⎢⎥
⎣⎦
3. x
2
+ y
2
+ 2xy 2xz + 2yz
Ans:
11 1
111
11 0
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
4. x
2
+ 4xy + 4y
2
+ 6xz + 5z
2
Ans:
123
240
305
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
Determine the quadratic for
m corresponding to the
symmetric matrix A =
(58)
00 1
5. 0 1 1
010
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
Ans: y
2
+ 2xz 2yz
210
6.
1 2 5
05
1
⎡⎤
⎢⎥
−−
⎢⎥
⎢⎥
⎣⎦
Ans: 2x
2
2y
2
+ z
2
2xy + 10yz
111
7.111
111
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
Ans: (
x + y + z)
2
410
8. 1 1 3
03
3
⎡⎤
⎢⎥
⎢⎥
⎢⎥
⎣⎦
Ans: 4x
2
2xy + 6yz + y
2
3z
2
Reduce the following quadratic form to canonical form by
diagonalisation: [JNTU 2000]
9. 6x
2
+ 3y
2
+ 3z
2
4yz 4zx 2xy
Ans: x
2
+ y
2
+ 7z
2
r = 3, s =
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Publisher Resources

ISBN: 9781299446557Publisher Website